Methodology and Statistics
Tilburg School of Social and Behavioral Sciences
Phone: 013-466 4030
Email Erwin Nagelkerke
Diagnostics for latent class models with dependent univariate and multivariate observations
Latent class (LC) analysis is used by social and behavioral scientists as a statistical method for building typologies, taxonomies, and classifications based on a set of observed characteristics. Examples include attitudinal typologies of citizens based on survey questions measuring their attitudes toward freedom of speech, subtypes of schizophrenia patients derived from recorded mood symptoms, classifications of developmental stages of children based on tests taken at different ages, taxonomies of delinquent youths derived from criminal records, classifications of consumers inferred from stated or revealed preferences, and taxonomies of temporal project networks based on characteristics of these projects and the related organizations.
The focus of this project is on allowing or improving the traditional model-fitting strategy in which diagnostics are used to check whether model assumptions hold, and if this is not the case to inform how the model should be modified. Local fit statistics that allow this approach are currently not available for several types of LC models, such as multilevel LC models and latent Markov models. The data sets to which these models are applied contain two types of dependencies, namely between the multiple responses of one individual and between the responses of different persons belonging to the same group, or for longitudinal data, between the multiple responses at one time point and between the responses at different time points.
Since the local independence assumption central to multilevel LC models implies that all responses should be independent of one another given the higher- and lower-level class memberships, diagnostics are required to test this. For the lower-level, local independence diagnostics can be very similar to those developed for standard LC models. However, special diagnostics should be developed to check whether associations between lower-level units belonging to the same higher-level units are detected correctly by the specified LC model.
Similar diagnostics may be developed for univariate cases. In such applications the assumption is that the nested responses are independent of one another conditional on the class membership of the individual or group. An example would be LC regression models, where tests for residual within-group associations between responses are required.
Prof. dr. J.K. Vermunt
Dr. D. Oberski
1 February 2013 – 31 January 2017